The Surface Area of the Surface $z = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

The surface area of the surface $z = x ^ { 2 } + y ^ { 2 }$ below z = 4 is

A) $\frac { \pi ( 11 \sqrt { 11 } - 1 ) } { 6 }$
B) $\frac { \pi ( 13 \sqrt { 13 } - 1 ) } { 6 }$
C) $\frac { \pi ( 15 \sqrt { 15 } - 1 ) } { 6 }$
D) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 6 }$
E) $\frac { \pi ( 19 \sqrt { 19 } - 1 ) } { 6 }$